[Condorman]

For the math, it does not matter if the data sequences naturally in small groups that come together at later times, or one after another in one large group.
In the end, either process is eventually going to produce an output string of a certain length.
Our math is then looking inside that output string to see if our correct data sequence(s) is/are evident.
And that is mathematically valid whether the data sequences itself one datum after another or in various sized groups of data one after another.

I would direct your attention to post #373 which partially addresses this point. The article also makes the (invalid) assumption that each trial takes place in a historical vaccuum; that for each consecutive trial, one sequence is exactly as likely to occur as any other sequence. Feedback mechanisms inherent in natural systems produce a bias that this mathematical model does not address.

[Southack]

"The article also makes the (invalid) assumption that each trial takes place in a historical vaccuum; that for each consecutive trial, one sequence is exactly as likely to occur as any other sequence. Feedback mechanisms inherent in natural systems produce a bias that this mathematical model does not address." - Condorman

That's not what the author said. The original scenario that he proposed had data being generated chaoticly. As that data was generated, the author calculated the probability/improbability of 41 characters sequencing in the correct order in any part of that entire data stream. Thus, for the desired result, there is no "historical vaccum" because the entire history of the data is being examined by the math.

As for your comment on "feedback systems", you've got two large hurdles to overcome: First, you have to show that a particular feedback system was in place prior to the very first life form becoming animated, and Second, you've got to demonstrate that such a feedback mechanism could actually change the probability / improbability of useful data self-forming from a chaotic environment.

Frankly, I doubt that either of those two hurdles could be overcome, and even if they were properly managed, would probably not alter the final mathematical result substantially.

Someone also made the flawed comment that the math didn't account for data forming in groups, and then those groups joining with each other, but that too is addressed in the math. To wit: whether you flip four coins at once or one coin at a time, the odds of getting all heads remains precisely the same. So too with data self-forming from a chaotic environment